After an even first-half, the game burst to life when former Royals James Henry and Darius Henderson combined for the latter to head past Adam Federici with 49 minutes gone.
John Marquis then doubled Millwall's advantage 10 minutes later to leave Reading staring at a sixth straight season without an opening day win.
However, Manset came off the bench and saved a point for Royals with a long-range strike and then a header into the top corner with five minutes remaining.
It was a sensational finish to a compelling match and both sets of fans applauded their teams off the pitch at the final whistle.
Reading will be looking for a first win of the Championship season when they travel to Leicester City next Saturday (3pm), with a Carling Cup trip to Charlton before then on Tuesday evening (7.45pm).
While they didn't pick up all three points, Royals dispelled any fears of a Wembley hangover with a blistering start to the match and could have led inside the first minute were it not for the legs of David Forde.
The Millwall keeper did well to spread himself after Noel Hunt broke down the left and fired a half-volley across goal.
Kebe then had a decent opportunity when he was found wide open at the back post but he volleyed tamely wide of goal.
The visitors struggled to keep possession but they looked dangerous on the counter-attack and Hamer Bouazza drilled a low shot across the goal and just wide of the post.
The pace of the game did eventually die down and Reading saw a couple of shots blocked on the edge of the box after patient build-up.
Kebe looked the liveliest player on the pitch with his probing runs down the right and he showed his speed to reach a long ball from Andy Griffin, only for Jem Karacan to blast the pull back over the bar.
Former Reading player Henry did the same at the other end on a couple of occasions and McAnuff also saw a shot fly into the stands before the break.
The start of the second-half was almost a carbon copy of the first, except it was Millwall who created the chances and they, unlike Royals, finished them.
First, Henry crossed for a wide open Henderson to head past Adam Federici and then, 10 minutes later, Marquis beat the Aussie goalkeeper with a back-post header.
In between the quickfire brace, Shane Long went close to equalising with a 25-yard shot that struck the bar and Kebe fizzed a cross across goal that Noel Hunt went close to poking in.
However, with a two-goal lead, Millwall kept the ball better than they had done in the first-half and Royals struggled to break them down.
In a bid to get back into the match, Brian McDermott threw on Hal Robson-Kanu and Manset for Karacan and Hunt, with McAnuff moving into the centre of the pitch
It wasn't until the final 10 minutes that the home team came to life though, with McAnuff serving warning of what was to come with a thunderous shot that struck the post.
Despite the late onslaught, however, Henderson could have secured the three points for Millwall when he broke the offside trap and, in acres of space, drilled a shot at Federici.
A few minutes later, Reading had their first goal of the season when substitute Manset cut in from the right and lashed a shot past Forde in the Millwall goal.
And the Frenchman grabbed his second goal not long after when headed a lofted Kebe cross into the corner.
Just as the earlier brace had got the visiting fans jumping, Manset's double breathed life into the home supporters.
However, that could have been sucked out of them on two occasions late on as Chris Hackett fired a ball across goal that Henderson was inches away from tapping in and then, in injury time, Scott Barron's shot was well saved by Federici.